DMUs were certainly used on a regular basis on the Bristol TM - Mangotsfield - Bath Green Park local trains. Of the S&D proper - the book 'Somerset & Dorset Swansong' refers to a railtour on 10.5.58 using a three car Swindon Cross Country DMU from Bath to Templecombe, and a DMU shuttle operated on 9.6.61 from Bath to Wellow in connection with a Jazz festival. On 6.4.68 a mixed four car unit on an RCTS tour traversed the short remaining section to Writhington Colliery near Radstock, and possibly other DMU tours did this bit too. I am unsure if, after passenger closure, a DEMU ever reached Blandford from Poole on a railtour?
I suspect, with a very large dose of hindsight, the best (most economical and likely to generate the most useful intermediate traffic) way of serving Bournemouth - Bristol (and further afield) flows [ as much as they may have been] would have been retention of the Salisbury-West Moors-Wimborne section (pity the line didn't serve Ringwood directly). Of course this was a bucolic little used byway at the time, and never [to my knowledge] traversed by a DEMU or DMU.
In the book 'Lightweight DMUs' by Evan Green-Hughes, there is a photograph (P68) of 4 x 2 car set climbing out of Bath Green Park through Lyncombe Vale to the Devonshire Tunnel on a Birmingham-Bournemouth excursion. No date unfortunately. Must have traversed the whole S&D mainline. What a trip......